Create a second Display State. With it active, expand the tree to show the columns for Hide/Show, Display Mode, Appearances, etc. In the Display Mode column, leave the parts you want shaded set to Default. Change the rest to "Wireframe".

Go back to the drawing view's PropertyManager, choose the new Display State, and select Shaded with Edges in the Display Style section. That should do what you need. I didn't test it with an exploded view, but I assume it works the same way.

This works fine, but for some reason it doesn't work the opposite way (ie. changing the parts I want highlighted to "shaded with edges" and then using a wireframe drawing view. It works in the model, but not the drawing.

The reason to do it this way, is simply that I want to highlight 6 parts out of 200, so it's MUCH easier to change the display state of only 6 parts. Is this by design or a bug?

A downfall to what I'm doing is that I can't "hide/show" part edges because it's not supported in shaded view. It would be nice to clean up a very busy drawing view. It's difficult to show leaders going through so many edges on the way to the target object, etc.

This works fine, but for some reason it doesn't work the opposite way (ie. changing the parts I want highlighted to "shaded with edges" and then using a wireframe drawing view. It works in the model, but not the drawing.

The reason to do it this way, is simply that I want to highlight 6 parts out of 200, so it's MUCH easier to change the display state of only 6 parts. Is this by design or a bug?

I'm pretty sure you will need to have the drawing view set to one of the shaded views to get any of the components to show as shaded.